EP 0 949 105 A1 discloses a vehicle in which a rear shelf, designated there by the reference number 14, is situated in front of a roof stowage space that is toward the rear in relation to the direction of travel, and below a rear window, and can be recessed along with the roof when it is opened. The rear shelf 14 is rigidly anchored to the rear roof section, therefore when this roof section is in the stowed position, said shelf is disposed nearly vertically, as is shown in FIG. 7. During folding, the forward roof section must maintain sufficient spacing from the rear roof section to avoid colliding with the protruding rear shelf. The stowed roof therefore requires a great deal of vertical stowage space, which decreases the size of the remaining trunk space. This problem is especially serious in side areas of the rear section of the roof located crosswise toward the exterior, since these areas project a considerable distance in the direction of travel when the roof is closed due to the crowning of the rear roof section, thus when the roof is stowed they project as far upward as the entire space between there and the backrest 4 that is to be covered by the rear shelf 14 when the roof is closed.